College Physics: A Strategic Approach

Randall D. Knight, Brian Jones, Stuart Field

Chapter 10

Energy and Work - all with Video Answers

Educators

+ 5 more educators

Chapter Questions

Problem 1

A 2.0 kg book is lying on a 0.75-m-high table. You pick it up and place it on a bookshelf $2.3 \mathrm{m}$ above the floor. During this process,
a. How much work does gravity do on the book?
b. How much work does your hand do on the book?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 2

The two ropes seen in Figure $\mathrm{P} 10.2$ are used to lower a $255 \mathrm{kg}$ piano exactly $5 \mathrm{m}$ from a second-story window to the ground. How much work is done by each of the three forces?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 4

You are pulling a child in a wagon. The rope handle is inclined upward at a $60^{\circ}$ angle. The tension in the handle is $20 \mathrm{N}$. How much work do you do if you pull the wagon $100 \mathrm{m}$ at a constant speed?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 5

A boy flies a kite with the string at a $30^{\circ}$ angle to the horizontal. The tension in the string is $4.5 \mathrm{N}$. How much work does the string do on the boy if the boy
a. Stands still?
b. Walks a horizontal distance of $11 \mathrm{m}$ away from the kite?
c. Walks a horizontal distance of 11 m toward the kite?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 6

A typical muscle fiber is $2.0 \mathrm{cm}$ long and has a cross-section area of $3.1 \times 10^{-9} \mathrm{m}^{2} .$ When the muscle fiber is stimulated, it pulls with a force of $1.2 \mathrm{mN}$. What is the work done by the muscle fiber as it contracts to a length of $1.6 \mathrm{cm} ?$

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 7

A crate slides down a ramp that makes a $20^{\circ}$ angle with the ground. To keep the crate moving at a steady speed, Paige pushes back on it with a $68 \mathrm{N}$ horizontal force. How much work does Paige do on the crate as it slides $3.5 \mathrm{m}$ down the ramp?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 8

A wind turbine works by slowing the air that passes its blades and converting much of the extracted kinetic energy to electric energy. A large wind turbine has $45-\mathrm{m}$ -radius blades. In typical conditions, $92,000 \mathrm{kg}$ of air moves past the blades every second. If the air is moving at $12 \mathrm{m} / \mathrm{s}$ before it passes the blades and the wind turbine extracts $40 \%$ of this kinetic energy, how much energy is extracted every second?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 9

At what speed does a 1000 kg compact car have the same kinetic energy as a $20,000 \mathrm{kg}$ truck going $25 \mathrm{km} / \mathrm{h} ?$

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 10

A 60 kg runner in a sprint moves at 11 m/s. A 60 kg cheetah in a sprint moves at $33 \mathrm{m} / \mathrm{s} .$ By what factor does the kinetic energy of the cheetah exceed that of the human runner?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 11

A car is traveling at $10 \mathrm{m} / \mathrm{s}$.
a. How fast would the car need to go to double its kinetic energy?
b. By what factor does the car's kinetic energy increase if its speed is doubled to $20 \mathrm{m} / \mathrm{s}$ ?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 12

II The opposite of a wind turbine is an electric fan: The electric energy that powers the fan is converted to the kinetic energy of moving air. A fan is putting $1.0 \mathrm{J}$ of kinetic energy into the air every second. Then the fan speed is increased by a factor of 2. Air moves through the fan faster, so the fan moves twice as much air at twice the speed. How much kinetic energy goes into the air every second?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 13

How fast would an $80 \mathrm{kg}$ man need to run in order to have the same kinetic energy as an 8.0 g bullet fired at $400 \mathrm{m} / \mathrm{s} ?$

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 14

A fielder tosses a 0.15 kg baseball at $32 \mathrm{m} / \mathrm{s}$ at a $30^{\circ}$ angle to the horizontal. What is the ball's kinetic energy at the start of its motion? What is the kinetic energy at the highest point of its arc?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 15

Sam's job at the amusement park is to slow down and bring to a stop the boats in the log ride. If a boat and its riders have a mass of $1200 \mathrm{kg}$ and the boat drifts in at $1.2 \mathrm{m} / \mathrm{s}$, how much work does Sam do to stop it?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 16

A school has installed a modestly-sized wind turbine. The three blades are $4.6 \mathrm{m}$ long; each blade has a mass of $45 \mathrm{kg}$. You can assume that the blades are uniform along their lengths. When the blades spin at 240 rpm, what is the kinetic energy of the blade assembly?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 17

The turntable in a microwave oven has a moment of inertia of $0.040 \mathrm{kg} \cdot \mathrm{m}^{2}$ and rotates continuously, making a complete revolution every $4.0 \mathrm{s}$. What is its kinetic energy?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 18

A typical meteor that hits the earth's upper atmosphere has a mass of only 2.5 g, about the same as a penny, but it is moving at an impressive 40 $\mathrm{km} / \mathrm{s} .$ As the meteor slows, the resulting thermal energy makes a glowing streak across the sky, a shooting star. The small mass packs a surprising punch. At what speed would a $900 \mathrm{kg}$ compact car need to move to have the same kinetic energy?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 19

An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.0 MJ when the flywheel is rotating at 20,000 revolutions per minute. What is the moment of inertia of the flywheel?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 20

The lowest point in Death Valley is $85.0 \mathrm{m}$ below sea level. The summit of nearby Mt. Whitney has an elevation of $4420 \mathrm{m}$. What is the change in gravitational potential energy of an energetic $65.0 \mathrm{kg}$ hiker who makes it from the floor of Death Valley to the top of Mt. Whitney?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 21

The world's fastest humans can reach speeds of about $11 \mathrm{m} / \mathrm{s} .$ In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 22

A 72 kg bike racer climbs a 1200 -m-long section of road that has a slope of $4.3^{\circ} .$ By how much does his gravitational potential energy change during this climb?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 23

A 1000 kg wrecking ball hangs from a 15 -m-long cable. The ball is pulled back until the cable makes an angle of $25^{\circ}$ with the vertical. By how much has the gravitational potential energy of the ball changed?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 24

How far must you stretch a spring with $k=1000 \mathrm{N} / \mathrm{m}$ to store $200 \mathrm{J}$ of energy?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 25

How much energy can be stored in a spring with a spring constant of $500 \mathrm{N} / \mathrm{m}$ if its maximum possible stretch is $20 \mathrm{cm} ?$

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 26

The spring in a retractable ballpoint pen is $1.8 \mathrm{cm}$ long, with a $300 \mathrm{N} / \mathrm{m}$ spring constant. When the pen is retracted, the spring is compressed by $1.0 \mathrm{mm} .$ When you click the button to extend the pen, you compress the spring by an additional $6.0 \mathrm{mm}$. How much energy is required to extend the pen?

Prabhu Ramji

Numerade Educator

Problem 27

The elastic energy stored in your tendons can contribute up to $35 \%$ of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch $41 \mathrm{mm},$ while nonathletes' stretch only 33 mm. The spring constant for the tendon is the same for both groups, $33 \mathrm{N} / \mathrm{mm} .$ What is the difference in maximum stored energy between the sprinters and the nonathletes?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 28

II Scallops use muscles to close their shells. Opening the shell is another story-muscles can only pull, they can't push. Instead of muscles, the shell is opened by a spring, a pad of a very elastic biological material called abduction. When the shell closes, the pad compresses; a restoring force then pushes the shell back open. The energy to open the shell comes from the elastic energy that was stored when the shell was closed. Figure $\mathrm{P} 10.28$ shows smoothed data for the restoring force of an abduction pad versus the compression. When the shell closes, the pad compresses by $0.15 \mathrm{mm} .$ How much elastic potential energy is stored?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 29

Mark pushes his broken car $150 \mathrm{m}$ down the block to his friend's house. He has to exert a 110 N horizontal force to push the car at a constant speed. How much thermal energy is created in the tires and road during this short trip?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 30

When you skid to a stop on your bike, you can significantly heat the small patch of tire that rubs against the road surface. Suppose a person skids to a stop by hitting the brake on his back tire, which supports half the $80 \mathrm{kg}$ combined mass of the bike and rider, leaving a skid mark that is $40 \mathrm{cm}$ long. Assume a coefficient of kinetic friction of $0.80 .$ How much thermal energy is deposited in the tire and the road surface?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 31

A 900 N crate slides 12 m down a ramp that makes an angle of $35^{\circ}$ with the horizontal. If the crate slides at a constant speed, how much thermal energy is created?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 32

If you slide down a rope, it's possible to create enough thermal energy to burn your hands or your legs where they grip the rope. Suppose a $40 \mathrm{kg}$ child slides down a rope at a playground, descending $2.0 \mathrm{m}$ at a constant speed. How much thermal energy is created as she slides down the rope?

Nicholas Mogoi

Numerade Educator

Problem 33

A 25 kg child slides down a playground slide at a constant speed. The slide has a height of $3.0 \mathrm{m}$ and is $7.0 \mathrm{m}$ long. Using the law of conservation of energy, find the magnitude of the kinetic friction force acting on the child.

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 34

Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square $1.8 \mathrm{m}$ on a side, with a drag coefficient of $1.4 .$ A runner completes a 200 m run at $5.0 \mathrm{m} / \mathrm{s}$ with this chute trailing behind. How much thermal energy is added to the air by the drag force?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 35

A boy reaches out of a window and tosses a ball straight up with a speed of $10 \mathrm{m} / \mathrm{s}$. The ball is $20 \mathrm{m}$ above the ground as he releases it. Use conservation of energy to find
a. The ball's maximum height above the ground.
b. The ball's speed as it passes the window on its way down.
c. The speed of impact on the ground.

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 36

The famous cliff divers of Acapulco leap from a perch $35 \mathrm{m}$ above the ocean. How fast are they moving when they reach the water surface? What happens to their kinetic energy as they slow to a stop in the water?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 37

What minimum speed does a 100 g puck need to make it to the top of a frictionless ramp that is $3.0 \mathrm{m}$ long and inclined at $20^{\circ} ?$

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 38

You can, in an emergency, start a manual transmission car by putting it in neutral, letting the car roll down a hill to pick up speed, then putting it in gear and quickly letting out the clutch. If the car needs to be moving at $3.5 \mathrm{m} / \mathrm{s}$ for this to work, how high a hill do you need? (You can ignore friction and drag.)

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 39

A $1500 \mathrm{kg}$ car is approaching the hill shown in Figure $\mathrm{P} 10.39$ at $10 \mathrm{m} / \mathrm{s}$ when it suddenly runs out of gas.
a. Can the car make it to the top of the hill by coasting?
b. If your answer to part a is yes, what is the car's speed after coasting down the other side?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 40

A 480 g peregrine falcon reaches a speed of $75 \mathrm{m} / \mathrm{s}$ in a vertical dive called a stoop. If we assume that the falcon speeds up under the influence of gravity only, what is the minimum height of the dive needed to achieve this speed?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 41

II A fireman of mass $80 \mathrm{kg}$ slides down a pole. When he reaches the bottom, $4.2 \mathrm{m}$ below his starting point, his speed is $2.2 \mathrm{m} / \mathrm{s} .$ By how much has thermal energy increased during his slide?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 42

A $20 \mathrm{kg}$ child slides down a $3.0-\mathrm{m}$ -high playground slide. She starts from rest, and her speed at the bottom is $2.0 \mathrm{m} / \mathrm{s}$.
a. What energy transfers and transformations occur during the slide?
b. What is the total change in the thermal energy of the slide and the seat of her pants?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 43

A hockey puck is given an initial speed of $5.0 \mathrm{m} / \mathrm{s}$. If the coefficient of kinetic friction between the puck and the ice is $0.05,$ how far does the puck slide before coming to rest? Solve this problem using conservation of energy.

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 44

Monica pulls her daughter Jessie in a bike trailer. The trailer and Jessie together have a mass of 25 kg. Monica starts up a $100-\mathrm{m}-\mathrm{long}$ slope that's $4.0 \mathrm{m}$ high. On the slope, Monica's bike pulls on the trailer with a constant force of $8.0 \mathrm{N}$. They start out at the bottom of the slope with a speed of $5.3 \mathrm{m} / \mathrm{s}$ What is their speed at the top of the slope?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 45

In the winter activity of tubing, riders slide down snowcovered slopes while sitting on large inflated rubber tubes. To get to the top of the slope, a rider and his tube, with a total mass of $80 \mathrm{kg},$ are pulled at a constant speed by a tow rope that maintains a constant tension of $340 \mathrm{N}$. How much thermal
energy is created in the slope and the tube during the ascent of a $30-\mathrm{m}-\mathrm{high}, 120-\mathrm{m}-\mathrm{long}$ slope?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 46

II Mosses don't spread by dispersing seeds; they disperse tiny spores. The spores are so small that they will stay aloft and move with the wind, but getting them to be windborne requires the moss to shoot the spores upward. Some species do this by using a spore-containing capsule that dries out and shrinks. The pressure of the air trapped inside the capsule increases. At a certain point, the capsule pops, and a stream of spores is ejected upward at $3.6 \mathrm{m} / \mathrm{s},$ reaching an ultimate height of $20 \mathrm{cm} .$ What fraction of the initial kinetic energy is converted to the final potential energy? What happens to the "lost" energy?

Donald Albin

Numerade Educator

Problem 47

A cyclist is coasting at $12 \mathrm{m} / \mathrm{s}$ when she starts down a $450-\mathrm{m}-\mathrm{long}$ slope that is $30 \mathrm{m}$ high. The cyclist and her bicycle have a combined mass of $70 \mathrm{kg}$. A steady $12 \mathrm{N}$ drag force due to air resistance acts on her as she coasts all the way to the bottom. What is her speed at the bottom of the slope?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

When you stand on a trampoline, the surface depresses below equilibrium, and the surface pushes up on you, as the data for a real trampoline in Figure $\mathrm{P} 10.48$ show. The linear variation of the force as a function of distance means that we can model the restoring force as that of a spring. A 72 kg gymnast jumps on the trampoline. At the lowest point of his motion, he is $0.80 \mathrm{m}$ below equilibrium. If we assume that all of the energy stored in the trampoline goes into his motion, how high above this lowest point will he rise?

Rashmi Sinha

Numerade Educator

Problem 49

The 5.0 -m-long rope in Figure $\mathrm{P} 10.49$ hangs vertically from a tree right at the edge of a ravine. A woman wants to use the rope to swing to the other side of the ravine. She runs as fast as
she can, grabs the rope, and swings out over the ravine.
a. As she swings, what energy conversion is taking place?
b. When she's directly over the far edge of the ravine, how much higher is she than when she started?
c. Given your answers to parts a and b, how fast must she be running when she grabs the rope in order to swing all the way across the ravine?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 50

The Special Olympics raises money through "plane pull" events in which teams of 25 people compete to see who can pull a $74,000 \mathrm{kg}$ airplane $3.7 \mathrm{m}$ across the tarmac. The inertia of the plane is an issue-but so is the $14,000 \mathrm{N}$ rolling friction force that works against the teams. If a team pulls with a constant force and moves the plane $3.7 \mathrm{m}$ in $6.1 \mathrm{s}$ (an excellent time), what fraction of the team's work goes to kinetic energy and what fraction goes to thermal energy?

Vishal Gupta

Numerade Educator

Problem 51

Figure $\mathrm{P} 10.51$ is the potential-energy diagram for a $20 \mathrm{g}$ particle that is released from rest at $x=1.0 \mathrm{m} .$
a. Will the particle move to the right or to the left? How can you tell?
b. What is the particle's maximum speed? At what position does it have this speed?
c. Where are the turning points of the motion?

Narayan Hari

Numerade Educator

Problem 52

For the potential-energy diagram in Figure $\mathrm{P} 10.52,$ what is the maximum speed of a $2.0 \mathrm{g}$ particle that oscillates between $x=2.0 \mathrm{mm}$ and $x=8.0 \mathrm{mm} ?$

Darren Wilson

Numerade Educator

Problem 53

At normal temperatures and pressures, hydrogen gas is composed of $\mathrm{H}_{2}$ molecules. An energy diagram for a hydrogen molecule appears in Figure P10.53. Use this information to answer Problems 10.53 and 10.54
How far apart are the individual atoms in a molecule of $\mathrm{H}_{2} ?$

Narayan Hari

Numerade Educator

Problem 54

What energy photon is needed to dissociate a molecule of $\mathrm{H}_{2} ?$

Daniel Gosser

Numerade Educator

Problem 55

II A 50 g marble moving at $2.0 \mathrm{m} / \mathrm{s}$ strikes a $20 \mathrm{g}$ marble at rest. What is the speed of each marble immediately after the collision? Assume the collision is perfectly elastic and the marbles collide head-on.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 56

Ball $1,$ with a mass of 100 g and traveling at $10 \mathrm{m} / \mathrm{s},$ collides head-on with ball $2,$ which has a mass of $300 \mathrm{g}$ and is initially at rest. What are the final velocities of each ball if the collision is (a) perfectly elastic? (b) perfectly inelastic?

Vishal Gupta

Numerade Educator

Problem 57

An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. What fraction of the first glider's initial kinetic energy is transformed into thermal energy in this collision?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 58

Two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. If the incoming ball has a speed of $200 \mathrm{m} / \mathrm{s},$ what are the final speed and direction of each ball if
a. The incoming ball is much more massive than the stationary ball?
b. The stationary ball is much more massive than the incoming ball?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

a. How much work must you do to push a $10 \mathrm{kg}$ block of steel across a steel table at a steady speed of $1.0 \mathrm{m} / \mathrm{s}$ for $3.0 \mathrm{s} ?$ The coefficient of kinetic friction for steel on steel is $0.60 .$
b. What is your power output while doing so?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

A shooting star is actually the track of a meteor, typically a small chunk of debris from a comet that has entered the earth's atmosphere. As the drag force slows the meteor down, its kinetic energy is converted to thermal energy, leaving a glowing trail across the sky. A typical meteor has a surprisingly small mass, but what it lacks in size it makes up for in speed. Assume that a meteor has a mass of $1.5 \mathrm{g}$ and is moving at an impressive $50 \mathrm{km} / \mathrm{s},$ both typical values. What power is generated if the meteor slows down over a typical 2.1 s? Can you see how this tiny object can make a glowing trail that can be seen hundreds of kilometers away?

Jared Enns

Numerade Educator

Problem 61

a. How much work does an elevator motor do to lift a
$1000 \mathrm{kg}$ elevator a height of $100 \mathrm{m}$ at a constant speed?
b. How much power must the motor supply to do this in $50 \mathrm{s}$ at constant speed?

Rashmi Sinha

Numerade Educator

Problem 62

$\mathrm{A} 500 \mathrm{kg}$ horse can provide a steady output power of $750 \mathrm{W}$ (that is, 1 horsepower) when pulling a load. How about a 38 kg sled dog? Data show that a $38 \mathrm{kg}$ dog can pull a sled that requires a pulling force of $60 \mathrm{N}$ at a steady $2.2 \mathrm{m} / \mathrm{s}$. What are the specific power values for the dog and the horse? What is the minimum number of dogs needed to provide the same power as one horse?

Averell Hause

Carnegie Mellon University

Problem 63

A 1000 kg sports car accelerates from 0 to $30 \mathrm{m} / \mathrm{s}$ in $10 \mathrm{s}$. . What is the average power of the engine?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 64

A world-class sprinter running a $100 \mathrm{m}$ dash was clocked at $5.4 \mathrm{m} / \mathrm{s} 1.0 \mathrm{s}$ after starting running and at $9.8 \mathrm{m} / \mathrm{s} 1.5 \mathrm{s}$ later. In
which of these time intervals, 0 to 1.0 s or 1.0 s to 2.5 s, was his output power greater?

Penny Riley

Numerade Educator

Problem 65

An elite Tour de France cyclist can maintain an output power of $450 \mathrm{W}$ during a sustained climb. At this output power, how long would it take an $85 \mathrm{kg}$ cyclist (including the mass of his bike) to climb the famed 1100 -m-high Alpe d'Huez mountain stage?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

$\mathrm{A}$ 70 kg human sprinter can accelerate from rest to $10 \mathrm{m} / \mathrm{s}$ in $3.0 \mathrm{s}$. During the same time interval, a $30 \mathrm{kg}$ greyhound can accelerate from rest to $20 \mathrm{m} / \mathrm{s}$. What is the specific power for each of these athletes?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 67

$\mathrm{A} 710 \mathrm{kg}$ car drives at a constant speed of $23 \mathrm{m} / \mathrm{s}$. It is subject to a drag force of 500 N. What power is required from the car's engine to drive the car
a. On level ground?
b. Un a hill with a slone of $2.0^{\circ} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 68

$\mathrm{A} 95 \mathrm{kg}$ quarterback accelerates a $0.42 \mathrm{kg}$ ball from rest to $24 \mathrm{m} / \mathrm{s}$ in $0.083 \mathrm{s} .$ What is the specific power for this toss?

Clifford Francis

Clifford Francis

Numerade Educator

Problem 69

An elevator weighing $2500 \mathrm{N}$ ascends at a constant speed of $8.0 \mathrm{m} / \mathrm{s} .$ How much power must the motor supply to do this?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 70

Humans can produce an output power as great as $20 \mathrm{W} / \mathrm{kg}$ during extreme exercise. Sloths are not so energetic. At its maximum speed, a 4.0 kg sloth can climb a height of $6.0 \mathrm{m}$ in 2.0 min. What's the specific power for this climb?

Surjit Tewari

Numerade Educator

Problem 71

$\mathrm{A} 550 \mathrm{kg}$ elevator accelerates upward at $1.2 \mathrm{m} / \mathrm{s}^{2}$ for the first $15 \mathrm{m}$ of its motion. How much work is done during this part of its motion by the cable that lifts the elevator?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 72

The energy yield of a nuclear weapon is often defined in terms of the equivalent mass of a conventional explosive. 1 ton of a conventional explosive releases 4.2 GJ. A typical nuclear warhead releases 250,000 times more, so the yield is expressed as 250 kilotons. I'hat is a staggering explosion, but the asteroid impact that wiped out the dinosaurs was significantly greater. Assume that the asteroid was a sphere $10 \mathrm{km}$ in diameter, with a density of $2500 \mathrm{kg} / \mathrm{m}^{3}$ and moving at $30 \mathrm{km} / \mathrm{s} .$ What energy was released at impact, in joules and in kilotons?

Narayan Hari

Numerade Educator

Problem 73

A $2.3 \mathrm{kg}$ box, starting from rest, is pushed up a ramp by a $10 \mathrm{N}$ force parallel to the ramp. The ramp is $2.0 \mathrm{m}$ long and tilted at $17^{\circ} .$ The speed of the box at the top of the ramp is $0.80 \mathrm{m} / \mathrm{s} .$ Consider the system to be the box $+\mathrm{ramp}+$ earth.
a. How much work $W$ does the force do on the system?
b. What is the change $\Delta K$ in the kinetic energy of the system?
c. What is the change $\Delta U_{\mathrm{g}}$ in the gravitational potential energy of the system?
d. What is the change $\Delta E_{\mathrm{th}}$ in the thermal energy of the system?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 74

$A \quad 55 \quad \mathrm{kg}$ skateboarder wants to just make it to the upper edge of a "half-pipe" with a radius of $3.0 \mathrm{m},$ as shown in Figure $\mathrm{P} 10.74$ What speed does he need at the bottom if he will coast all the way up? The skateboarder isn't a simple particle: Assume that his mass in a deep crouch is concentrated $0.75 \mathrm{m}$ from the half-pipe. If he remains in that position all the way up, what initial speed does he need to reach the upper edge?

Vishal Gupta

Numerade Educator

Problem 75

Fleas have remarkable jumping ability. A 0.50 mg flea, jumping straight up, would reach a height of $40 \mathrm{cm}$ if there were no air resistance. In reality, air resistance limits the height
to $20 \mathrm{cm}$
a. What is the flea's kinetic energy as it leaves the ground?
b. At its highest point, what fraction of the initial kinetic energy has been converted to potential energy?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 76

You are driving your $1500 \mathrm{kg}$ car at $20 \mathrm{m} / \mathrm{s}$ down a hill with a $5.0^{\circ}$ slope when a deer suddenly jumps out onto the roadway. You slam on your brakes, skidding to a stop. How far do you skid before stopping if the kinetic friction force between your tires and the road is $1.2 \times 10^{4} \mathrm{N}$ ? Solve this problem using conservation of energy.

Prashant Bana

Numerade Educator

Problem 77

$\mathrm{A} 20 \mathrm{kg}$ child is on a swing that hangs from $3.0-\mathrm{m}$ -long chains, as shown in Figure $\mathrm{P} 10.77 .$ What is her speed $v_{\mathrm{i}}$ at the bottom of the arc if she swings out to a $45^{\circ}$ angle before reversing direction?

Prashant Bana

Numerade Educator

Problem 78

Suppose you lift a $20 \mathrm{kg}$ box by a height of $1.0 \mathrm{m}$.
a. How much work do you do in lifting the box? Instead of lifting the box straight up, suppose you push it up a 1.0 -m-high ramp that makes a $30^{\circ}$ degree angle with the horizontal, as shown in Figure $\mathrm{P} 10.78 .$ Being clever, you choose a ramp with no friction.
b. How much force $F$ is required to push the box straight up the slope at a constant speed?
c. How long is the ramp?
d. Use your force and distance results to calculate the work you do in pushing the box up the ramp. How does this compare to your answer to part a?

Vishal Gupta

Numerade Educator

Problem 79

The sledder shown in Figure $\mathrm{P} 10.79$ starts from the top of a frictionless hill and slides down into the valley. What initial speed $v_{\mathrm{i}}$ does the sledder need to just make it over the next hill?

Prashant Bana

Numerade Educator

Problem 80

In a physics lab experiment, a spring clamped to the table shoots a 20 g ball horizontally. When the spring is compressed $20 \mathrm{cm},$ the ball travels horizontally $5.0 \mathrm{m}$ and lands on the floor $1.5 \mathrm{m}$ below the point at which it left the spring. What is the spring constant?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 81

The maximum energy a bone can absorb without breaking is surprisingly small. For a healthy human of mass $60 \mathrm{kg}$, experimental data show that the leg bones of both legs can absorb about $200 \mathrm{J}$
a. From what maximum height could a person jump and land rigidly upright on both feet without breaking his legs? Assume that all the energy is absorbed in the leg bones in a rigid landing.
b. People jump from much greater heights than this; explain how this is possible. Hint: Think about how people land when they jump from greater heights.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 82

In an amusement park water slide, people slide down an essentially frictionless tube. The top of the slide is $3.0 \mathrm{m}$ above the bottom where they exit the slide, moving horizontally, $1.2 \mathrm{m}$ above a swimming pool. What horizontal distance do they travel from the exit point before hitting the water? Does the mass of the person make any difference?

Prashant Bana

Numerade Educator

Problem 83

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass $m$ is fired into a block of mass $M .$ The block, with the embedded bullet, then slides across a frictionless table and collides with a horizon-
tal spring whose spring constant is $k$. The opposite end of the spring is anchored to a wall. The spring's maximum compression $d$ is measured.
a. Find an expression for the bullet's initial speed $v_{\mathrm{B}}$ in terms of $m, M, k,$ and $d$ Hint: This is a two-part problem. The bullet's collision with the block is an inelastic collision. What quantity is conserved in an inelastic collision? Subsequently the block hits a spring on a frictionless surface. What quantity is conserved in this collision?
b. What was the speed of a $5.0 \mathrm{g}$ bullet if the block's mass is $2.0 \mathrm{kg}$ and if the spring, with $k=50 \mathrm{N} / \mathrm{m},$ was compressed by $10 \mathrm{cm} ?$
c. What fraction of the bullet's initial kinetic energy is "lost"? Where did it go?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 84

Wores $A$ and $B$ in Figure $P 10.84$ have masses of $12.0 \mathrm{kg}$ and $4.0 \mathrm{kg}$, respectively. The two boxes are released from rest. Use conservation of energy to find the boxes' speed when box $\mathrm{B}$ has fallen a distance of $0.50 \mathrm{m}$. Assume a frictionless upper surface.

Prashant Bana

Numerade Educator

Problem 85

Two coupled boxcars are rolling along at $2.5 \mathrm{m} / \mathrm{s}$ when they collide with and couple to a third, stationary boxcar.
a. What is the final speed of the three coupled boxcars?
b. What fraction of the cars' initial kinetic energy is transformed into thermal energy?

Hubert Agamasu

Numerade Educator

Problem 86

A 50 g ball of clay traveling at $6.5 \mathrm{m} / \mathrm{s}$ hits and sticks to a $1.0 \mathrm{kg}$ block sitting at rest on a frictionless surface.
a. What is the speed of the block after the collision?
b. Show that the mechanical energy is not conserved in this collision. What percentage of the ball's initial kinetic energy is "lost"? Where did this kinetic energy go?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 87

A package of mass $m$ is released from rest at a ware- house loading dock and slides down a 3.0 -m-high frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass $2 m,$ from the bottom of the chute as shown in Figure $\mathrm{P} 10.87$.
a. Suppose the packages stick together. What is their common speed after the collision?
b. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass $m$ rebound?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 88

Swordfish are capable of stunning output power for short bursts. A 650 kg swordfish has a cross-section area of $0.92 \mathrm{m}^{2}$ and a drag coefficient of $0.0091 \longrightarrow$ xceptionally low due to a number of adaptations. Such a fish can sustain a speed of $30 \mathrm{m} / \mathrm{s}$ for a few seconds. Assume seawater has a density of $1026 \mathrm{kg} / \mathrm{m}^{3}$. What is the specific power for motion at this high speed?

Carson Merrill

Numerade Educator

Problem 89

The mass of an elevator and its occupants is $1200 \mathrm{kg}$. The electric motor that lifts the elevator can provide a maximum power of $15 \mathrm{kW}$. What is the maximum constant speed at which this motor can lift the elevator?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 90

A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of $2.5 \mathrm{m}$ onto a concrete surface, a ball must rebound to a height of $1.4 \mathrm{m} .$ During impact, the ball compresses by approximately $6 \mathrm{mm}$.
How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.)
A. $5 \mathrm{m} / \mathrm{s}$
B. $7 \mathrm{m} / \mathrm{s}$
C. $25 \mathrm{m} / \mathrm{s}$
D. $50 \mathrm{m} / \mathrm{s}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 91

If the ball accelerates uniformly when it hits the floor, what is its approximate acceleration as it comes to rest before rebounding?
A. $1000 \mathrm{m} / \mathrm{s}^{2}$
B. $2000 \mathrm{m} / \mathrm{s}^{2}$
C. $3000 \mathrm{m} / \mathrm{s}^{2}$
D. $4000 \mathrm{m} / \mathrm{s}^{2}$

Vysakh M

Numerade Educator

Problem 92

The ball's kinetic energy just after the bounce is less than just before the bounce. In what form does this lost energy end up?
A. Elastic potential energy
B. Gravitational potential energy
C. Thermal energy
D. Rotational kinetic energy

Surjit Tewari

Numerade Educator

Problem 93

By approximately what percent does the kinetic energy decrease?
A. $35 \%$
B. $45 \%$
C. $55 \%$
D. $65 \%$

Dheeraj Sharma

Numerade Educator

Problem 94

When a tennis ball bounces from a racket, the ball loses approximately $30 \%$ of its kinetic energy to thermal energy. A ball that hits a racket at a speed of $10 \mathrm{m} / \mathrm{s}$ will rebound with approximately what speed?
A. $8.5 \mathrm{m} / \mathrm{s}$
B. $7.0 \mathrm{m} / \mathrm{s}$
C. $4.5 \mathrm{m} / \mathrm{s}$
D. $3.0 \mathrm{m} / \mathrm{s}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 95

When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section $5.6,$ the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that $F \propto v^{2}$ exactly and that the air is motionless with respect to the ground unless noted Suppose a cyclist and her bicycle have a combined mass of $60 \mathrm{kg}$ and she is cycling along at a speed of $5 \mathrm{m} / \mathrm{s}$.
If the drag force on the cyclist is $10 \mathrm{N},$ how much energy does she use in cycling $1 \mathrm{km} ?$
A. $6 \mathrm{kJ}$
B. $10 \mathrm{kJ}$
C. $50 \mathrm{kJ}$
D. $100 \mathrm{kJ}$

Vishal Gupta

Numerade Educator

Problem 96

Under these conditions, how much power does she expend as she cycles?
A. $10 \mathrm{W}$
B. $50 \mathrm{W}$
C. $100 \mathrm{W}$
D. $200 \mathrm{W}$

Supratim Pal

Numerade Educator

Problem 97

If she doubles her speed to $10 \mathrm{m} / \mathrm{s},$ how much energy does she use in cycling $1 \mathrm{km} ?$
A. $20 \mathrm{kJ}$
B. $40 \mathrm{kJ}$
C. $200 \mathrm{kJ}$
D. $400 \mathrm{kJ}$

Surjit Tewari

Numerade Educator

Problem 98

How much power does she expend when cycling at that speed?
A. $100 \mathrm{W}$
B. $200 \mathrm{W}$
C. $400 \mathrm{W}$
D. $1000 \mathrm{W}$

Supratim Pal

Numerade Educator

Problem 99

Upon reducing her speed back down to $5 \mathrm{m} / \mathrm{s},$ she hits a headwind of $5 \mathrm{m} / \mathrm{s} .$ How much power is she expending now?
A. $100 \mathrm{W}$
B. $200 \mathrm{W}$
C. $500 \mathrm{W}$
D. $1000 \mathrm{W}$

Vysakh M

Numerade Educator